Chapter 17 . Classification of Fish Stock-Recruitment Relationships 339
going forward until the SSE in (17.10) is obtained. Then in the backward pass, the
error rates for a. and ß propagate from the output end toward the input end, and the
estimates for a. and ß are updated based on the steepest gradient descent (17.11).
The proposed hybrid leaming algorithm is guaranteed to find the global optima
for the fuzzy parameters (i.e. aj , a z ' bj and bJ and also the FMF parameters (i.e. a.
and ß) if reasonable prior knowledge is available for the fuzzy membership
function, wh ich is most often the case. In fact, this hybrid leaming algorithm not
only decreases the dimension of the search space in the gradient method, but it
also substantially reduces the convergence time.
17.3.2
Bootstrap Re-sampling Procedure
For any reasonable and intelligent fisheries management implementation, it is
wise and prudent not only to give a point estimate for the fishery policy
parameters, but also to give a measure of the uncertainty for these management
policy parameters. The most commonly adopted measures are the standard errors,
confidence interval and even a probability distribution. Of course, if the
probability distribution can be obtained, the associated standard error and
confidence interval can be readily calculated. However, to my knowledge, this is
not a common practice in most machine-leaming methods. To address the lack of
uncertainty estimation in the machine-leaming models (the Fuzzy-SR model in
this paper), a bootstrap re-sampling scheme is proposed to produce a sampling
probability distribution for the stock parameters related to fishery management
policies so that the associated variance (or standard error) and confidence interval
can be obtained since bootstrap resampling is widely used to obtain such sampling
distributions. Efron and Tibshirani (1993), Shao and Tu (1995), and Davision and
Hinkley (1997) provide extensive theoretical backgrounds and plenty of examples.
In general, the available data (S" R,. SST.) to the Fuzzy-SR model can be
treated as either deterministic or random variables. In the ca se of deterministic
variables. the residuals CI = Y I - }>I • are assumed to be identically independently
distributed (i.i.d.) with a zero mean and a constant variance of cl. In the case of
random variables, data (S" R" SST,) are assumed to be i.i.d. with E( E,IS,. SST,)=O.
The above assumptions correspond to two different types of settings for bootstrap
resampling (Tibshirani 1994). One setting treats the inputs as fixed based on the
deterministic variables (S" SST,) with the model residuals c r = Y r -}>I as the
sampling units, which are called bootstrap residuals. The other setting treats each
data point (S" R" SST,) as a sampling unit, which is commonly called bootstrap
pairing. Since most SR data are intrinsically auto-correlated based on the spawner
and recruitment interactions. then the bootstrap residuals would be more
appropriate with the diagnostics of the residuals from the Fuzzy-SR model. This
bootstrap residuals re-sampling strategy involves following steps:
going forward until the SSE in (17.10) is obtained. Then in the backward pass, the
error rates for a. and ß propagate from the output end toward the input end, and the
estimates for a. and ß are updated based on the steepest gradient descent (17.11).
The proposed hybrid leaming algorithm is guaranteed to find the global optima
for the fuzzy parameters (i.e. aj , a z ' bj and bJ and also the FMF parameters (i.e. a.
and ß) if reasonable prior knowledge is available for the fuzzy membership
function, wh ich is most often the case. In fact, this hybrid leaming algorithm not
only decreases the dimension of the search space in the gradient method, but it
also substantially reduces the convergence time.
17.3.2
Bootstrap Re-sampling Procedure
For any reasonable and intelligent fisheries management implementation, it is
wise and prudent not only to give a point estimate for the fishery policy
parameters, but also to give a measure of the uncertainty for these management
policy parameters. The most commonly adopted measures are the standard errors,
confidence interval and even a probability distribution. Of course, if the
probability distribution can be obtained, the associated standard error and
confidence interval can be readily calculated. However, to my knowledge, this is
not a common practice in most machine-leaming methods. To address the lack of
uncertainty estimation in the machine-leaming models (the Fuzzy-SR model in
this paper), a bootstrap re-sampling scheme is proposed to produce a sampling
probability distribution for the stock parameters related to fishery management
policies so that the associated variance (or standard error) and confidence interval
can be obtained since bootstrap resampling is widely used to obtain such sampling
distributions. Efron and Tibshirani (1993), Shao and Tu (1995), and Davision and
Hinkley (1997) provide extensive theoretical backgrounds and plenty of examples.
In general, the available data (S" R,. SST.) to the Fuzzy-SR model can be
treated as either deterministic or random variables. In the ca se of deterministic
variables. the residuals CI = Y I - }>I • are assumed to be identically independently
distributed (i.i.d.) with a zero mean and a constant variance of cl. In the case of
random variables, data (S" R" SST,) are assumed to be i.i.d. with E( E,IS,. SST,)=O.
The above assumptions correspond to two different types of settings for bootstrap
resampling (Tibshirani 1994). One setting treats the inputs as fixed based on the
deterministic variables (S" SST,) with the model residuals c r = Y r -}>I as the
sampling units, which are called bootstrap residuals. The other setting treats each
data point (S" R" SST,) as a sampling unit, which is commonly called bootstrap
pairing. Since most SR data are intrinsically auto-correlated based on the spawner
and recruitment interactions. then the bootstrap residuals would be more
appropriate with the diagnostics of the residuals from the Fuzzy-SR model. This
bootstrap residuals re-sampling strategy involves following steps: